Scilab Function
Last update : July 2001

atan - 2-quadrant and 4-quadrant inverse tangent

### Calling Sequence

  `phi=atan(x)`
  `phi=atan(y,x)`

### Parameters

- `x`: real or complex scalar, vector or matrix
- `phi`: real or complex scalar, vector or matrix
- `x, y`: real scalars, vectors or matrices of the same size
- `phi`: real scalar, vector or matrix

### Description

The first form computes the 2-quadrant inverse tangent, which is the inverse of `tan(phi)`. For real `x`, `phi` is in the interval (-pi/2, pi/2). For complex `x`, `atan` has two singular, branching points `+%i`,`-%i` and the chosen branch cuts are the two imaginary half-straight lines [i, i*oo) and (-i*oo, -i].

The second form computes the 4-quadrant arctangent (atan2 in Fortran), this is, it returns the argument (angle) of the complex number `x+i*y`. The range of `atan(y,x)` is (-pi, pi].

For real arguments, both forms yield identical values if `x>0`.

In case of vector or matrix arguments, the evaluation is done element-wise, so that `phi` is a vector or matrix of the same size with `phi(i,j)=atan(x(i,j))` or `phi(i,j)=tan(y(i,j),x(i,j))`.

### Examples

    // examples with the second form
    x=[1,%i,-1,%i]
    phasex=atan(imag(x),real(x))
    atan(0,-1)
    atan(-%eps,-1)

    // branch cuts
    atan(-%eps + 2*%i)
    atan(+%eps + 2*%i)
    atan(-%eps - 2*%i)
    atan(+%eps - 2*%i)

    // values at the branching points
    ieee(2)
    atan(%i)
    atan(-%i)

### See Also

`tan`, `ieee`,

### Authors

  B.P.
  L.V.D. (authors of the complex atan function).